Sr Examen

Derivada de y=arctg(chx)+(chx)lnchx

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
atan(cosh(x)) + cosh(x)*log(cosh(x))
$$\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)} + \operatorname{atan}{\left(\cosh{\left(x \right)} \right)}$$
atan(cosh(x)) + cosh(x)*log(cosh(x))
Gráfica
Primera derivada [src]
  sinh(x)                                    
------------ + log(cosh(x))*sinh(x) + sinh(x)
        2                                    
1 + cosh (x)                                 
$$\log{\left(\cosh{\left(x \right)} \right)} \sinh{\left(x \right)} + \sinh{\left(x \right)} + \frac{\sinh{\left(x \right)}}{\cosh^{2}{\left(x \right)} + 1}$$
Segunda derivada [src]
                   2                                   2                     
  cosh(x)      sinh (x)                          2*sinh (x)*cosh(x)          
------------ + -------- + cosh(x)*log(cosh(x)) - ------------------ + cosh(x)
        2      cosh(x)                                          2            
1 + cosh (x)                                      /        2   \             
                                                  \1 + cosh (x)/             
$$\log{\left(\cosh{\left(x \right)} \right)} \cosh{\left(x \right)} + \frac{\sinh^{2}{\left(x \right)}}{\cosh{\left(x \right)}} + \cosh{\left(x \right)} + \frac{\cosh{\left(x \right)}}{\cosh^{2}{\left(x \right)} + 1} - \frac{2 \sinh^{2}{\left(x \right)} \cosh{\left(x \right)}}{\left(\cosh^{2}{\left(x \right)} + 1\right)^{2}}$$
Tercera derivada [src]
/                       2               2                 2              2        2                  \        
|         1         sinh (x)      6*cosh (x)        2*sinh (x)     8*cosh (x)*sinh (x)               |        
|4 + ------------ - -------- - --------------- - --------------- + ------------------- + log(cosh(x))|*sinh(x)
|            2          2                    2                 2                   3                 |        
|    1 + cosh (x)   cosh (x)   /        2   \    /        2   \      /        2   \                  |        
\                              \1 + cosh (x)/    \1 + cosh (x)/      \1 + cosh (x)/                  /        
$$\left(\log{\left(\cosh{\left(x \right)} \right)} - \frac{\sinh^{2}{\left(x \right)}}{\cosh^{2}{\left(x \right)}} + 4 + \frac{1}{\cosh^{2}{\left(x \right)} + 1} - \frac{2 \sinh^{2}{\left(x \right)}}{\left(\cosh^{2}{\left(x \right)} + 1\right)^{2}} - \frac{6 \cosh^{2}{\left(x \right)}}{\left(\cosh^{2}{\left(x \right)} + 1\right)^{2}} + \frac{8 \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{\left(\cosh^{2}{\left(x \right)} + 1\right)^{3}}\right) \sinh{\left(x \right)}$$
Gráfico
Derivada de y=arctg(chx)+(chx)lnchx